Detonation and deflagration initiation at the focusing of shock waves in combustible gaseous mixture

Abstract. Detonation and deflagration initiation under focusing conditions in a lean hydrogen-air mixture was experimentally investigated. The experiments were carried out in a shock tube equipped with the laser schlieren system and pressure transducers. Two-dimensional wedges (53° and 90°), semi-cylinder and parabola, were used as the focusing elements. The peculiarities of mild and strong ignition inside the reflector cavity were visualized. A hydrogen-nitrogen mixture was taken for comparison between reactive and inert mixture. It was found that mild ignition inside the reflector cavity can lead to detonation initiation outside the cavity. Schlieren pictures of the process were obtained and the dependence of the distance of detonation initiation on Mach number of the incident shock wave was established. Received 30 August 1999 / Accepted 23 February 2000     

Experimental investigation of the interaction of shock waves with textiles

Experimental studies have been performed to investigate the pressure amplification experienced behind a textile when exposed to a shock wave. Three textiles with different masses and air permeabilities were studied. Mach numbers for tests varied between 1.23 and 1.55. The distance between the back wall and the textile was varied between 3 and 15 mm. It was found that in most cases the presence of the textile led to a pressure amplification at the back wall. This amplification was dependent on the textile, Mach number and distance from the back wall. The processes causing the pressure amplification were identified by analysing pressure traces and contact shadowgraphs. It was found that when the incident wave impinges on the textile, a part is reflected upstream and a part is transmitted through the textile. The transmitted portion reflects back and forth in the gap between the textile and the back wall leading to a back wall pressure trace with a stepped profile. In addition, the textile moves towards the back wall causing compression waves to propagate towards the back wall. The combination of the stepped profile and the compression waves cause the pressure amplification. The contribution of each mechanism depends on the textile properties. Approximate wave diagrams have been constructed. Tests involving multiple layers of textiles are also discussed. Received 17 October 2000 / Accepted 2 February 2001     

Attenuation of shock waves propagating in polyurethane foams

Shock wave attenuation in polyurethane foams is investigated experimentally and numerically. This study is a part of research project regarding shock propagation in polyurethane foams with high-porosities = 0.951 ~ 0.977 and low densities of ρc = 27.6 ~55.8 kg/m³. Sixty Millimeter long cylindrical foams with various cell numbers and foam insertion condition were installed in a horizontal shock tube of 50 mm i.d. and 5.4 mm in length. Results of pressure measurements in air/foam combination are compared with CFD simulation solving the one-dimensional Euler equations. In the case of a foam B fixed on shock tube wall, pressures at the shock tube end wall increases relatively slowly comparing to non-fixed foam, free to move and a foam A fixed on shock tube wall. This implies that elastic inertia hardly contributes to pressure build up. Pressures behind a foam C fixed on shock tube wall decrease indicating that shock wave is degenerated into compression wave. Dimensionless impulse and attenuation factor decrease as the initial cell number increases. The momentum loss varies depending on cell structure and cell number.     

On the relation between particle velocity and shock wave speed for thermoelastic materials

Results of shock-wave experiments in solids often suggest a nearly-linear relation between the particle velocity behind the shock and the shock wave speed. The present note reconsiders the question of whether thermoelastic material models may be consistent with such observations. Emphasis is placed on the role played by the response of the material in severe compression, as distinguished from its response for small or moderate deformations. The details are illustrated for materials of Mie-Grüneisen type. Received 21 December 2001 / Accepted 22 April 2002 Published online 8 July 2002     

The reflected pressure field in the interaction of weak shock waves with a compressible foam

This paper deals with the waves that are reflected from slabs of porous compressible foam attached to a rigid wall when impacted by a weak shock wave. The interest is in establishing possible attenuation of the pressure field after a shock or blast wave has struck the surface. Foam densities from 14 to 38 kg/m³ were tested over a range of shock wave Mach numbers less than 1.4. It is shown that the initial reflected shock wave strength is accurately predicted by the pseudo-gas model of Gelfand et al. (1983), with a pressure ratio of approximately 80% of the value for reflection off a rigid wall. Evidence is presented of gas entering the foam during the early stages of the process. A second wave emerges from the foam at a later stage and is separated from the first by a region of constant velocity and pressure. This second wave is not a shock wave but a compression front of significant thickness, which emerges from the foam earlier than predicted by the pseudo-gas model. Analysis of the origin of this wave points to much more complex flows within the foam than previously assumed, particularly in an apparent decrease in average wave front speed as the foam is compressed. It is shown that the pressure ratio across both these waves taken together is slightly higher than that for reflection off a rigid wall. In some cases this compression wave train is followed by a weak expansion wave.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Propagation of converging and diverging shock waves under isothermal condition

In this article the flows of perfect gas behind converging and diverging strong shock waves under isothermal condition in the cases of spherical and cylindrical symmetry are examined. A diverging shock wave is formed by energy supply according to a power law. These waves propagate in a uniform medium at rest and all conservation laws hold at the fronts of these shock waves. It was established that in the case of converging waves for any value of the ratios of specific heats the solution of the problem under consideration exists and is unique. When the problem has more than one solution. In the case of diverging shock waves the solution exists and is unique for any from the interval and any value of power in the energy input law. Received 4 August 1996 / Accepted 28 May 1996     

Numerical investigation of the propagation of shock waves in rigid porous materials: flow field behavior and parametric study

A numerical parametric study of the flow field which develops when a planar shock wave impinge on a rigid porous material is presented. This study complements an earlier study (Levy et al. 1996a) where the values of some dominating parameters were estimated and the dependence of the resulting flow field on these values was not checked. Received 22 April 1996 / Accepted 5 January 1997     

Mesodynamics of shock waves in a polycrystalline metal

Simulation of the shock compression of polycrystalline α-iron at the mesoscale has been carried out using a two-dimensional, quasi-MD code. Grains of about 15 μm are randomly distributed to simulate the polycrystal. Results show the presence of a particle velocity dispersion comparable to the level observed experimentally. Other unique features include an eddy-like velocity field (meso rotation) and chaotic wave fronts. This paper was based on work that was presented at the 3rd international symposium on interdisciplinary shock wave research, Canberra, Australia, 1–3, March 2006.     

Numerical investigations of shock waves in gas-particle mixtures

The propagation of shock waves in gas-particle mixtures in one- and two-dimensional geometries is numerically investigated. Two schemes for approximating conservation laws for particles, which are collectively treated as a continuum medium, are compared and discussed. Different models of the drag coefficient and Nusselt number, directly affecting the interaction between the gas and particle phases, are used for obtaining shock profiles, and the results are compared. The oblique shock reflections at a solid wedge in a gas-particle mixture are simulated. The results demonstrate that the reflection pattern changes as the shock propagates along the wedge, revealing strong non-selfsimilarity of the phenomenon.Received: 22 May 2003, Accepted: 28 August 2003, Published online: 12 November 2003 Correspondence to:T. Saito     

Interaction of shock waves during the passage of a disrupted meteoroid through the atmosphere

The motion of fragments following disintegration of a meteoroid during its flight through the Earth's atmosphere is investiated. Shock wave configurations, aerodynamical forces and moments acting on each fragment and the trajectories of the pieces are determined for hypothetical initial configurations. The results of numerical simulations show that a meteoroid's breakup may lead to both increase and decrease of the total cross section, drag forces and energy release in the atmosphere. As a consequence the emitted radiation varies.     

Transformations of graphite and boron nitride in shock waves

Peculiarities of shock adiabat of graphite are attributed to the graphite–diamond transformation. However only a very small amount of diamond can be recovered from pure shocked graphite with a density approaching the theoretical value. In order to interpret this fact, accessible data concerning the behaviour of graphite under static and dynamic load have been analysed. An additional peculiarity of the shock adiabat of graphite has been found at 12 GPa by analysing compressibility data. It has been attributed to shearing in the basal planes that paves the way for deformation of the planes. An isotherm of cold compression of graphite can be constructed on the basis of the results from theoretical modelling published in the literature. Another isotherm, fitting experimental data, has been proposed. An isotherm for graphitic boron nitride has been also proposed. The isotherms have been used in the interpretation of the peculiarities of shock adiabats. It has been shown that the so-called “mixed-phase” region is an apparent compressibility curve. Energy evaluations based on the isotherms have proved that the peculiarities of the shock adiabat of graphite correspond to the formation of hexagonal instead of cubic diamond. Similarly the formation of the wurtzite modification of BN is responsible for the peculiarities of the shock adiabat of BN. Literature data concerning the mechanism of the polymorphous transformations of graphite and BN in shock waves have been reviewed. On the basis of proposed isotherms of cold compression, the activation energy has been appraised and an equation of kinetics proposed. The equation has been analysed by comparing results of theoretical modelling and accessible experimental data. Received 11 March 1993 / Accepted 15 September 1993     

Self-ignition and ignition of aluminum powders in shock waves

Ignition of fine aluminum powders in reflected shock waves has been studied. Two ignition regimes are found: self-ignition observed at temperatures higher than 1800 K and “low-temperature” ignition at temperatures of 1000–1800 K. The possibility of initiating the ignition of aluminum powders in air using combustible liquids has been studied too. Received 4 December 2000 / Accepted 30 May 2001     

Experimental studies of ignition and transition to detonation induced by the reflection and diffraction of shock waves

This paper presents results from a program of experimental studies of ignition induced by the interaction of an initially planar shock wave with an obstacle in its path. With the aid of pressure measurements, spark schlieren photography and smoked foil techniques it is shown how, given favourable initial conditions, the two-dimensional multiple shock reflection and diffraction can promote ignition and transition to detonation in reactive gaseous mixtures. Comparison of the results with those of a non-reactive gas distinguishes the gas dynamic and chemical processes involved, and experimentally determined detonation cell sizes are compared with values predicted using chemical kinetic rate data. The systems investigated were argon, air, propane-air, propane-oxygen-argon and ethylene-oxygen-argon. Received: 3 December 1998 / Accepted: 27 October 1999     

Evolution of shock waves and the primary vortex loop discharged from a square cross-sectional tube

In this paper, a numerical and experimental investigation of the evolution of a transmitting shock wave and its associated primary vortex loop, which are discharged from the open end of a square cross-sectional tube, is described. The experiments were conducted in the square tube connected to a diaphragmless shock tube and the flowfield was visualized from the axial direction with diffusive holographic interferometry. The numerical simulations were carried out by solving the three-dimensional Euler equations with a dispersion-controlled scheme. The numerical results were displayed in the form of interferograms to compare them with experimental interferograms. Good agreement between the numerical and experimental results was obtained. More detailed numerical calculations were carried out, from which the three-dimensional transition of the shock wave configuration from an initial planar to a spherical shape and the development of the primary vortex loop from a square shaped to a three-dimensional structure were clearly observed and interpreted. Received 29 January 1998 / Accepted 22 May 1998     

Enhancement of shock waves in a porous medium saturated with a liquid containing soluble-gas bubbles

Evolution of a moderate-intensity shock wave and its enhancement after reflection from a rigid surface embedded in a porous medium are studied experimentally. The medium is saturated with a liquid that has bubbles of a soluble gas. A physical mechanism of shock wave enhancement in a saturated porous medium is proposed. Experimental data on the amplitude and velocity of reflected waves are compared with results of theoretical modeling. The process of gas bubble dissolution behind a shock wave is studied.     

Theoretical considerations on shock reflections and their implications on the evaluation of air intake performance

Many theoretical studies have shown the existence of a hysteresis effect in the solution of oblique shock reflections. In fact, a wide domain of free-stream Mach number and shock angle values exists where regular reflection and Mach reflection are both possible solutions for the same flow conditions. Part of this domain overlaps the typical operating conditions of supersonic air intakes, and therefore it is of practical interest to obtain a deeper understanding of the theoretical problem. Indeed, although both solutions are theoretically possible, they yield very different flowfields and consequently large discrepancies in the evaluation of the air intake performance. Numerical solutions for steady configurations have been carried out and compared with the flow evolution obtained for time-dependent cases. The results have confirmed numerically the existence of the multiple solution domain where hysteresis takes place in time-dependent simulations. The analysis of the physical and numerical problems encountered has provided indications for a correct simulation in practical applications. Received 10 August 1999 / Accepted 6 October 2000     

Possibility of acceleration of the threshold processes for multi-component gas in the front of a shock wave

Studies of translational nonequilibrium in the front of a shock wave propagating in a three-component gas were performed by the Monte Carlo simulation method. Simulations were performed for mixtures of components with molecular mass ratios , and shock Mach number . The distribution of relative velocities for pairs of molecules of heavy low-concentration additives 2 and 3 substantially exceeded, in the front, its equilibrium values behind the wave at high values of . The maximum value of this superequilibrium was about for the numerical density ratio: 1000:1:1 and . Calculations showed that high values of the effect of superequilibrium take place up to a ratio of densities 200:1:1. Simulations performed for and a mixture of He, molecular oxygen and Xe with the numerical density ratio 200:1:1 showed also the high value of the superequilibrium effect at corresponding to dissociation threshold of oxygen. Thus, dissociation of oxygen by collisions with Xe in the front of a wave may have a considerably higher rate than total dissociation behind the wave. Received 4 August 1995 / Accepted 25 April 1996     

On the RR→MR transition of asymmetric shock waves in steady flows

In this paper, RR→MR transition of asymmetric shock waves has been theoretically studied. The transition can occur between the sonic-point and maximum-deflection criteria due to the the effects of expansion fans which are inherent flow structures. Comparison shows a better agreement among experiments and the analytical results. Some discrepancies reported in previous studies among experiments and theory have also been explained based on the threshold for RR→MR transition.      

Experimental and numerical studies of rotational relaxation behind a strong shock wave in air

This paper describes the experimental and numerical investigations of unknown characteristics of the rotational nonequilibrium phenomena behind a strong shock wave in air. Experiments were carried out using a piston-driven shock tube with helium as driving gas and air as driven (test) gas, operated as a two-stage shock tube. In the experiments, emission spectra of NO were measured to evaluate the rotational temperature behind a strong shock wave. The numerical calculations use the computational code for the thermal and chemical nonequilibrium flow behind a strong shock wave developed by the present author's group, where 11 chemical species (N, O, NO, N, O, N, O, NO, N, O, e) and 48 chemical reactions of high-temperature air are considered. The thermal nonequilibrium is expressed by introducing an 8 temperature model composed of translational temperature, rotational and vibrational temperatures for N, O, NO, and electron temperature. The coupling of a rotation, vibration and dissociation (CRVD) model was incorporated to take sufficiently into account the rotational nonequilibrium. The calculations were conducted for the same conditions as the experimental ones. From the calculated flow properties, emission spectra were re-constructed using the code for computing spectra of high temperature air “SPRADIAN”. Furthermore, rotational and vibrational temperatures of NO (0,1) were determined from a curve fitting method and compared with the computed results. Received 12 September 2001 / Accepted 18 February 2002     

传统Spar平台垂荡主共振时非线性耦合响应的研究

考虑瞬时波面影响,建立了Spar平台垂荡-纵摇运动的参数激励耦合运动方程,应用多尺度法导出了波浪频率接近垂荡固有频率时响应方程的一阶摄动解并做数值验证。计算结果显示:当波浪高度达到一定值时,纵摇运动中出现大量的亚谐频率成分;随着波浪高度进一步增大,纵摇运动将出现明显的幅值跳跃现象。研究结果表明,能量渗透现象是纵摇运动失稳的主要原因,波浪激励力矩对于纵摇本身的贡献很小。由于垂荡模态存在能量饱和现象,多余的垂荡能量将会向纵摇模态转移,导致出现大幅值的纵摇运动。